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We study conformational properties of a single multi-block copolymer chain consisting of flexible (F) and semi-flexible (S) blocks with equal composition of F- and S-units and with different affinity to a solvent. We perform Monte Carlo (MC) simulations based on the stochastic approximation Monte Carlo (SAMC) algorithm [1,2] which is one of the most recent realizations of the flat-histogram-type MC algorithms [3]. Such algorithms are based on the idea of equally frequent sampling of all energy states of the system and accumulating the density of states function. They sample the configuration space of molecular systems much more uniformly than standard importance sampling MC methods (like, e.g., Boltzmann sampling in canonical MC simulations), and are a powerful tool for obtaining accurate information on phase transitions in molecular systems [3]. In our realization of SAMC algorithm [4-7], we use the two-dimensional density of states function, which depends on the energy of intramolecular stiffness and on the energy of non-valence interactions. We present data on different non-trivial globular morphologies, including several structures with high orientational ordering of bonds, which we have obtained in our model for different values of the chain length, the block length and the stiffness parameter. Diagrams of states (pseudo-phase diagrams) in variables temperature vs. stiffness parameter are presented for different values of the block length. We compare our results with those obtained previously for a single SF-copolymer chain in a non-selective solvent [4-6] and discuss the observed differences [7]. We also present our recent results on the aggregation behavior of several flexible- semiflexible multi-block copolymer chains and discuss the possibility of shape- persistent aggregation.